Step-by-step Solution:

We know that: \[ \sinh x = \frac{e^x - e^{-x}}{2} \] and \[ \cosh x = \frac{e^x + e^{-x}}{2} \] Now, consider the integral: \[ \int e^x (\sinh x + \cosh x) \, dx = \int e^x (e^x) \, dx = \frac{e^{2x}}{2} + C \] The expression \( e^x (\cosh x) \) can be written as: \[ e^x \left( \frac{e^x + e^{-x}}{2} \right) = \frac{e^{2x}}{2} + C \] Hence, the answer is: \[ e^x \cosh x \]